Drug Targeting Organ-Specific Strategies

13.2 Pharmacokinetics and Pharmacodynamics, Modelling, Simulation, and Data Analysis 339
These models have relatively few parameters, and the parameters have a limited physiological
or anatomical meaning. For example, a compartmental volume relates the quantity of the
drug to its concentration in a compartment, and does not refer to an anatomically- or physiologically-defined
area of the body.
The differential equations defining a compartmental model are derived from logical and
simple principles. As an example, consider a model with two compartments as depicted in
Figure 13.1.The change in the quantity of a drug in a compartment is the net result of the rate
of entry of the drug, that is, the sum of the amount of drug administered to the compartment
(for example, an intravenous infusion) or formed within the compartment (for example, release
from a drug–carrier conjugate) and the rate of transport from other compartments, reduced
by the rate of exit, that is, the sum of the rates of removal from the compartment by
elimination or by transport to other compartments.
The rate of transport from a certain compartment is governed by the concentration in that
compartment and a proportionality constant, denoted (elimination or distribution) clearance
(dimension: volume time -1 ) as formulated below.
V 1 · dC 1 = R1 + CL 21 · C 2 – CL 12 · C 1 – CL 10 · C 1
dt
(13.1)
where V 1 is the apparent volume of compartment 1, C 1 is the drug concentration in compartment
1, R 1 is the rate of drug administration or drug release in compartment 1, CL 12 is
the distribution clearance from compartment 1 to compartment 2, and CL 10 is the elimination
clearance from compartment 1.
Usually, it is assumed that there is no net transport between two compartments if the concentrations
in both compartments are equal; in this specific case CL 21 = CL 12.
Similar equations can be written for compartment 2. The same principle can be applied to
any compartmental model, irrespective of its complexity.
R1
central
compartment
V1
k10
k12
k21
peripheral
compartment
Figure 13.2. Compartmental model based on rate constants (Section 13.2.4.1). The drug is administered
at a rate R 1 into the central compartment, which is characterized by a volume of distribution V 1. The
drug is transported to and from the peripheral compartment with rate constants k 12 and k 21, respectively.
The peripheral compartment is characterized by a volume of distribution V 2 (usually it is assumed that
there is no net transport between the two compartments if the concentrations in both compartments are
equal; in this case k 21 · V 2 = k 12 · V 1). Elimination may take place from both compartments and is
characterized by rate constants k 10 and k 20, respectively.
V2
k20